Question

18.
Graph the relation {(5, 0), (0, 5), (5, 1), (1, 5)}. Is it a function? Why or why not?

Answer 1

To determine if the relation \(\{(5, 0), (0, 5), (5, 1), (1, 5)\}\) is a function, we need to check if each input (the first element of each ordered pair) corresponds to exactly one output (the second element of each ordered pair).

Let's look at the ordered pairs in the relation:

1. \( (5, 0) \)
2. \( (0, 5) \)
3. \( (5, 1) \)
4. \( (1, 5) \)

Notice that the input \(5\) has two different outputs:
- In the pair \( (5, 0) \), the output is \(0\).
- In the pair \( (5, 1) \), the output is \(1\).

Since the input \(5\) corresponds to two different outputs (\(0\) and \(1\)), this violates the definition of a function, which states that each input must map to exactly one output.

Therefore, the relation is **not a function** because there are two pairs that have the same first element (input \(5\)) but different second elements (outputs \(0\) and \(1\)).